volume | PIER Journals

Abstract

The 3D Berenger's and uniaxial perfectly matched layers used for the truncation of the FDTD computations are theoretically investigated respectively in the discrete space, including numerical dispersion and impedance characteristics. Numerical dispersion for both PMLs is different from that of the FDTD equations in the normal medium due to the introduction of loss. The impedance in 3D homogeneous Berenger's PML medium is the same as that in the truncated normal medium even in the discrete space, however, the impedance in 3D homogenous UPML medium is different, but the discrepancy smoothly changes as the loss in the UPML medium slowly change. Those insights acquired can help to understand why both 3D PMLs can absorb the outgoing wave with arbitrary incidence, polarization, and frequency, but with different efficiency.

1. Taflove, A., Advances in Computational Electrodynamics, the Finite-Difference Time-Domain Method, 1998.

2. Mur, G., "Absorbing boundary conditions for the finitedifference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromagn. Compat., Vol. 23, 377-382, 1981. Google Scholar

3. Liao, Z. P., H. L. Wong, B. Yang, and Y. Yuan, "A transmitting boundary for transient wave analyses," Scientia Sinica, Vol. 27, 1063-1076, 1984. Google Scholar

4. Mei, K. K. and J. Fang, "Superabsorption â€” a method to improve absorbing boundary conditions," IEEE Trans. Antennas Propagat., Vol. 40, 1001-1010, 1992.
doi:10.1109/8.166524 Google Scholar

5. Teixeira, F. L. and W. C. Chew, "Differential forms, metrics, and the reflectionless absorption of electromagnetic waves," Journal of Electromagnetic Waves and Applications, Vol. 13, 665-686, 1999. Google Scholar

6. Buksas, M. W., "Implementing the perfectly matched layer absorbing boundary condition with mimetic differencing schemes," Progress In Electromagnetics Research, Vol. 32, 383-411, 2001.
doi:10.2528/PIER00080115 Google Scholar

7. Li, L. W., P. S. Kooi, M. S. Leong, and S. T. Chew, "FDTD analysis of sidecoupled microstrip filter," Journal of Electromagnetic Waves and Applications, Vol. 14, 1533-1548, 2000. Google Scholar

8. Berenger, J., "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 114, 185-200, 1994.
doi:10.1006/jcph.1994.1159 Google Scholar

9. Berenger, J., "Three dimensional perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 127, 363-379, 1996.
doi:10.1006/jcph.1996.0181 Google Scholar

10. Chew, W. C. and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Microwave and Optical Technology Letters, Vol. 7, 599-604, 1994. Google Scholar

11. Gedney, S. D., "An anisotropic perfectly matched layer absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antennas and Propagat., Vol. 44, 1630-1639, 1996.
doi:10.1109/8.546249 Google Scholar

12. Tang, J., K. D. Paulsen, and S. A. Haider, "Perfectly matched layer mesh terminations for nodal-based finite element methods in electromagnetic scattering," IEEE Trans. Antennas and Propagat., Vol. 46, 507-516, 1998.
doi:10.1109/8.664114 Google Scholar

13. Pena, N. and M. M. Ney, "Absorbing boundary conditions using perfectly matched layer (PML) technique for three-dimensional TLM simulations," IEEE Trans. Microwave Theory Tech., Vol. 45, 1749-1755, 1997.
doi:10.1109/22.641722 Google Scholar

14. Qi, Q. and T. L. Geers, "Evaluation of perfectly matched layer for computational acoustics," Journal of Computational Physics, Vol. 139, 166-183, 1998.
doi:10.1006/jcph.1997.5868 Google Scholar

15. Prescott, D. T. and N. V. Shuley, "Reflection analysis of FDTD boundary conditions â€” Part II: Berenger's PML absorbing layers," IEEE Trans. Microwave Theory Tech., Vol. 45, 1171-1178, 1997.
doi:10.1109/22.618404 Google Scholar

Dr. Weiliang Yuan

Professor Er Ping Li